S3W4 Vectors and Polar Coordinate review

Last updated 8 months ago

22 questions

1

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S3W4 Vectors and Polar Coordinate review

Last updated 8 months ago

22 questions

1

Draggable item		Corresponding Item

1

You have an aleks assignment - it is optional. work on it and then report back here - what questions do you think you would like to work on in class?

1

below are pairs of vectors written in different forms. Match the vectors on the left to their pair on the right.

Draggable item		Corresponding Item

		\vec{u} has an terminal point at (14,3) and an initial point at (8,-9)

		from the x-axis

To find the magnitude of a vector in component form, you simply

add the magnitudes of the components

use pythagorean theorem with the components

take the inverse tan of the coefficient of \hat{j} over the coefficient of \hat{i}

Divide the components by the angle

To find the angle of the vector from the horizontal axis,

add the magnitudes of the components

use pythagorean theorem with the components

take the inverse tan of the coefficient of \hat{j} over the coefficient of \hat{i}

Divide the components by the magnitude

To find the component form of the unit vector in the direction of a vector you simply

add the magnitudes of the components

use pythagorean theorem with the components

take the inverse tan of the coefficient of \hat{j} over the coefficient of \hat{i}

Divide the components by the magnitude

To find the dot product of two vectors you

multiply the \hat{i} components together and make that the coefficient of the \hat{i}, and multiply the \hat{j} components together and make that the coefficient of the \hat{j}

multiply the \hat{i} components together and multiply the \hat{j} components together and then add those products together. 

multiply both components by the scalar

Multiply the \hat{i} component by the \hat{j} and vice-versa. then add them together

To find if two vectors are parallel you

determine the \frac{delta y}{delta x} of both vectors and see if they are equal

determine the \frac{delta y}{delta x} of both vectors and see if they are reciprocal of each other

take the dot product to determine if it is equal to 0

take the dot product to determine if it is equal to the magnitude of one of the vectors

To find if two vectors are perpendicular you

determine the \frac{delta y}{delta x} of both vectors and see if they are equal

determine the \frac{delta y}{delta x} of both vectors and see if they are reciprocal of each other

take the dot product to determine if it is equal to 0

take the dot product to determine if it is equal to the magnitude of one of the vectors

given two vectors in component form, you can find the angle between them by

take the inverse tan of \hat{i} components divided by the\hat{j} components and then add those angles

find the dot product using the component equation, divide by the product of the magnitudes of both vectors, then take the inverse cosine

using pythagorean theorem

graphing and using a protractor is the only way

When you are finding the component form of a vector \vec{u} given as a magnitude and an angle \theta from the positive x axis you would

||\vec{u}||\cdot\hat{i}+||\vec{u}||\hat{j}

 <r\sin\theta, r\cos\theta>

 <magnitude\cdot\cos\theta, magnitude\cdot\sin\theta>

Which of these is finding the component of \vec{u} along \vec{v}

(\vec{u}\cdot\hat{v})\hat{v}

both of the above will work

neither of the above will work

in polar coordinates r stands for

the x coordinate

the y coordinate

the distance between your point and the origin

the angle from the x-axis

in polar coordinates \theta stands for

the x coordinate

the y coordinate

the distance between your point and the origin

the angle from the x-axis

in polar coordinates r\cos\theta is the

the x coordinate

the y coordinate

the distance between your point and the origin

the angle from the x-axis

in polar coordinates r\sin\theta is the

the x coordinate

the y coordinate

the distance between your point and the origin

the angle from the x-axis

when converting a polar equation into a rectangular equation I simply

Replace x and y with  r\cos\theta and r\sin\theta respectively and then solve for r

Replace x and y with  r\cos\theta and r\sin\theta respectively and then solve for \theta

replace r and \theta with \sqrt{x^2+y^2} and \tan^{-1} respectively then solve for y

replace r and \theta with \sqrt{x^2+y^2} and \tan^{-1} respectively then simplify, possibly using completing the square to consolidate x terms and y terms

What does De Moivre's Theorem relate?

Angles and trigonometry

Real numbers and polynomials

Complex numbers and powers

Vectors and magnitudes

Which formula represents De Moivre's Theorem?

a^n + b^n = (a + b)^n

\sin^2 x + \cos^2 x = 1

(\cos \theta + i\sin \theta)^n = (\cos n\theta + i\sin n\theta)

a^2 + b^2 = c^2

In De Moivre's Theorem, 'n' represents what?

Any integer

Rational numbers

Only odd numbers

Only even numbers

De Moivre's Theorem applies to which type of numbers?

Real numbers

Rational numbers

Whole numbers

Complex numbers

You have an aleks assignment - it is optional. work on it and then report back here - what questions do you think you would like to work on in class?

below are pairs of  vectors written in different forms. Match the vectors on the left to their pair on the right. 

\vec{u} has an terminal point at (14,3) and an initial point at (8,-9)

from the x-axis

To find the magnitude of a vector in component form, you simply

add the magnitudes of the components

use pythagorean theorem with the components

take the inverse tan of the coefficient of \hat{j} over the coefficient of \hat{i}

Divide the components by the angle

To find the angle of the vector from the horizontal axis, 

add the magnitudes of the components

use pythagorean theorem with the components

take the inverse tan of the coefficient of \hat{j} over the coefficient of \hat{i}

Divide the components by the magnitude

To find the component form of the unit vector in the direction of a vector you simply

add the magnitudes of the components

use pythagorean theorem with the components

take the inverse tan of the coefficient of \hat{j} over the coefficient of \hat{i}

Divide the components by the magnitude

To find the dot product of two vectors you 

multiply the \hat{i} components together and make that the coefficient of the \hat{i}, and multiply the \hat{j} components together and make that the coefficient of the \hat{j}

multiply the \hat{i} components together and multiply the \hat{j} components together and then add those products together. 

multiply both components by the scalar

Multiply the \hat{i} component by the \hat{j} and vice-versa. then add them together

To find if two vectors are parallel you

determine the \frac{delta y}{delta x} of both vectors and see if they are equal

determine the \frac{delta y}{delta x} of both vectors and see if they are reciprocal of each other

take the dot product to determine if it is equal to 0

take the dot product to determine if it is equal to the magnitude of one of the vectors

To find if two vectors are perpendicular you

determine the \frac{delta y}{delta x} of both vectors and see if they are equal

determine the \frac{delta y}{delta x} of both vectors and see if they are reciprocal of each other

take the dot product to determine if it is equal to 0

take the dot product to determine if it is equal to the magnitude of one of the vectors

given two vectors in component form, you can find the angle between them by 

take the inverse tan of \hat{i} components divided by the\hat{j} components and then add those angles

find the dot product using the component equation, divide by the product of the magnitudes of both vectors, then take the inverse cosine

using pythagorean theorem

graphing and using a protractor is the only way

When you are finding the component form of a vector \vec{u} given as a magnitude and an angle \theta from the positive x axis you would

||\vec{u}||\cdot\hat{i}+||\vec{u}||\hat{j}

 <r\sin\theta, r\cos\theta>

 <magnitude\cdot\cos\theta, magnitude\cdot\sin\theta>

Which of these is finding the component of \vec{u} along \vec{v}

(\vec{u}\cdot\hat{v})\hat{v}

both of the above will work

neither of the above will work

in polar coordinates r stands for 

the x coordinate

the y coordinate

the distance between your point and the origin

the angle from the x-axis

in polar coordinates \theta stands for 

the x coordinate

the y coordinate

the distance between your point and the origin

the angle from the x-axis

in polar coordinates r\cos\theta is the

the x coordinate

the y coordinate

the distance between your point and the origin

the angle from the x-axis

in polar coordinates r\sin\theta is the

the x coordinate

the y coordinate

the distance between your point and the origin

the angle from the x-axis

when converting a polar equation into a rectangular equation I simply

Replace x and y with  r\cos\theta and r\sin\theta respectively and then solve for r

Replace x and y with  r\cos\theta and r\sin\theta respectively and then solve for \theta

replace r and \theta with \sqrt{x^2+y^2} and \tan^{-1} respectively then solve for y

replace r and \theta with \sqrt{x^2+y^2} and \tan^{-1} respectively then simplify, possibly using completing the square to consolidate x terms and y terms

What does De Moivre's Theorem relate?

Angles and trigonometry

Real numbers and polynomials

Complex numbers and powers

Vectors and magnitudes

Which formula represents De Moivre's Theorem?

a^n + b^n = (a + b)^n

\sin^2 x + \cos^2 x = 1

(\cos \theta + i\sin \theta)^n = (\cos n\theta + i\sin n\theta)

a^2 + b^2 = c^2

In De Moivre's Theorem, 'n' represents what?

Any integer

Rational numbers

Only odd numbers

Only even numbers

De Moivre's Theorem applies to which type of numbers?

Real numbers

Rational numbers

Whole numbers

Complex numbers